Spontaneous squeezing of a vortex in an optical lattice

Martikainen, Jani-Petri; Stoof, H. T. C.

doi:10.1103/physreva.70.013604

Cited by 12 publications

(14 citation statements)

References 32 publications

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“…To impose the linear phase variation to the order parameter, one can impose a linear phase variation [26,27,36] to the Hamiltonian. Here M α indicates the number of lattice sites in direction alpha, i.e., the total volume the lattice V = M x M y M z d 3 This variation corresponds small (Θ α is small) superfluid velocity, which is given by…”

Section: Superfluid Densitymentioning

confidence: 99%

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Superfluid density of the ultra-cold Fermi gas in optical lattices

Paananen¹

2009

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. In this paper we study the superfluid density of the two component Fermi gas in optical lattices with population imbalance. Three different type of phases, the BCS-state (Bardeen, Cooper, and Schrieffer), the FFLO-state (Fulde, Ferrel, Larkin, and Ovchinnikov), and the Sarma state, are considered. We show that the FFLO superfluid density differs from the BCS/Sarma superfluid density in an important way. Although there are dynamical instabilities in the FFLO phase, when the interaction is strong or densities are high, on the weak coupling limit the FFLO phase is found to be stable.

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Section: Superfluid Densitymentioning

confidence: 99%

“…One can make the unitary transformation [26,27,36], which corresponds the local transformationĉ σ,i →ĉ σ,i e iΘ·R i , and the twisted Hamiltonian becomeŝ…”

Section: Superfluid Densitymentioning

confidence: 99%

Superfluid density of the ultra-cold Fermi gas in optical lattices

Paananen¹

2009

J. Phys. B: At. Mol. Opt. Phys.

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“…In this Letter we propose to combine these three topics to engineer a superstring in the laboratory, i.e., a line-like quantum object with both bosonic and fermionic excitations and a supersymmetric hamiltonian that is invariant under interchanges of these excitations. The physics of a vortex line in a one-dimensional optical lattice has been studied recently [13,14]. Because of the optical lattice, the transverse quantum fluctuations of the vortex line are greatly enhanced in this configuration.…”

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confidence: 99%

“…In our superstring realization there are also bosonboson and boson-fermion interactions. The kelvons interact repulsively among each other when Ω < Ω c [14]. In addition, a repulsive interaction between the kelvons and the fermionic atoms is generated by the fact that physically the presence of a kelvon means that the vortex core moves off center, together with the fermions trapped in it.…”

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confidence: 99%

Ultracold Superstrings in Atomic Boson-Fermion Mixtures

2005

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We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry. DOI: 10.1103/PhysRevLett.95.250401 PACS numbers: 03.75.Mn, 11.25.ÿw, 32.80.Pj, 67.40.ÿw In recent years, three topics have, in particular, attracted a lot of attention in the area of ultracold atomic gases. These topics are vortices [1][2][3][4][5], boson-fermion mixtures [6 -10], and optical lattices [11,12]. In this Letter we propose to combine these three topics to engineer a superstring in the laboratory, i.e., a linelike quantum object with both bosonic and fermionic excitations and a supersymmetric Hamiltonian that is invariant under interchanges of these excitations. The physics of a vortex line in a onedimensional optical lattice has been studied recently [13,14]. Because of the optical lattice, the transverse quantum fluctuations of the vortex line are greatly enhanced in this configuration. The vortex can therefore be viewed as a quantum mechanical string and it forms the bosonic part of our superstring. In addition, we propose to trap fermionic atoms in the vortex core, to make a nonrelativistic version of a so-called Green-Schwarz superstring in four spacetime dimensions. Because our ultracold superstring is nonrelativistic, it is not constrained to the ten-dimensional spacetimes in which superstrings are usually studied in highenergy physics. The precise mathematical connection with string theory is currently under investigation.Apart from the connection to string theory, our ultracold superstring is also of interest in its own right. To the best of our knowledge, it is the first condensed-matter system proposed where supersymmetry can be studied experimentally. The intriguing possibility of observing effects of supersymmetry is common in high-energy physics, but novel in a condensed-matter setting. In this particular case, the supersymmetry protects the superstring from spiraling out of the gas. This can be understood from the fact that the dissipation resulting in this motion has two sources, namely, the creation of two additional bosons in the transverse oscillations of the vortex, and the production of an additional particle-hole pair of fermions. At the supersymmetric point these two contributions interfere destructively and the stability of the superstring is greatly enhanced. Moreover, the ultracold superstring allows for the study of a quantum phase transition that spontaneously breaks supersymmetry. Experimentally this will be directly visible by observing the superstring spiraling out of the center of the gas. Note that supersymmetry can only be real...

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“…[18] we discussed the equilibrium properties of a straight vortex when the interaction term is attractive and pointed out that in this case the quantum mechanical state of the vortex can become strongly squeezed. However, here make the usual classical approximation and study the nonlinear excitations of the vortex line.…”

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Vortex-Line Solitons in A Periodically Modulated Bose-Einstein Condensate

Martikainen

Stoof

2004

Phys. Rev. Lett.

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We study the nonlinear excitations of a vortex line in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the classical Euler dynamics of the vortex results in a description of the vortex line in terms of a (discrete) one-dimensional Gross-Pitaevskii equation, which allows for both bright and gray soliton solutions. We discuss these solutions in detail and predict that it is possible to create vortex-line solitons with current experimental capabilities.

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Spontaneous squeezing of a vortex in an optical lattice

Cited by 12 publications

References 32 publications

Superfluid density of the ultra-cold Fermi gas in optical lattices

Superfluid density of the ultra-cold Fermi gas in optical lattices

Ultracold Superstrings in Atomic Boson-Fermion Mixtures

Vortex-Line Solitons in A Periodically Modulated Bose-Einstein Condensate

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